Ergodic Optimization in the Expanding Case (eBook, PDF) - Garibaldi, Eduardo
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This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study of optimizing probability measures. This work presents and discusses the fundamental concepts of the theory, including the use and relevance of Sub-actions as analogues to subsolutions of the Hamilton-Jacobi equation. Further, it provides evidence for the impressively broad applicability of the tools inspired by the weak KAM theory.

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Produktbeschreibung
This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study of optimizing probability measures. This work presents and discusses the fundamental concepts of the theory, including the use and relevance of Sub-actions as analogues to subsolutions of the Hamilton-Jacobi equation. Further, it provides evidence for the impressively broad applicability of the tools inspired by the weak KAM theory.

Autorenporträt
Eduardo Garibaldi holds a PhD in Mathematics from the Federal University of Rio Grande do Sul, Brazil, and an MA from the IMPA – National Institute for Pure and Applied Mathematics, Brazil, having pursued postdoctoral studies at the Université Bordeaux, France. He is currently affiliated with the University of Campinas, Brazil, and his research efforts chiefly focus on dynamical systems and ergodic theory, motivated by problems from equilibrium statistical mechanics and solid state physics.